The computational modeling and simulation of acoustic spaces is fundamental to many scientific and engineering applications [10]. The demands vary widely, from interactive simulation in computer games and virtual reality to highly accurate computations for offline applications, such as architectural design and engineering. Acoustic spaces may correspond to indoor spaces with complex geometric representations (such as multi-room environments, automobiles, or aircraft cabins), or to outdoor spaces corresponding to urban areas and open landscapes.
Computational acoustics has been an area of active research for almost half a century and is related to other fields (such as seismology, geophysics, meteorology, etc.) that deal with similar wave propagation through different mediums. Small variations in air pressure (the source of sound) are governed by the three-dimensional wave equation, a second-order linear partial differential equation. The computational complexity of solving this wave equation increases as at least the cube of frequency, and is a linear function of the volume of the scene. Given the auditory range of humans (20 Hz-20 kHz), performing wave-based acoustic simulation for acoustic spaces corresponding to a large environment, such as concert hall or a cathedral (e.g. volume of 10,000-15,000 m3) for the maximum simulation frequency of 20 kHz requires tens of Exaflops of computational power and tens of terabytes of memory. In fact, wave-based numeric simulation of the high frequency wave equation is considered one of the more challenging problems in scientific computation[13].
Current acoustic solvers are based on either geometric or wave-based techniques. Geometric methods, which are based on image source methods or ray-tracing and its variants [2, 14, 28], do not accurately model certain low-frequency features of acoustic propagation, including diffraction and interference effects. The wave-based techniques, on the other hand, directly solve governing differential or integral equations which inherently account for wave behavior. Some of the widely-used techniques are the finite-difference time domain method (FDTD) [25, 6], finite-element method (FEM) [31], equivalent source method (ESM) [18], or boundary-element method (BEM) [9, 8]. However, these solvers are mostly limited to low-frequency (less than 2 kHz) acoustic wave propagation for larger architectural or outdoor scenes, as higher-frequency simulation on these kinds of scenes requires extremely high computational power and terabytes of memory. Hybrid techniques also exist which take advantage of the strengths of both geometric and wave-based propagation[35].
Recently developed low-dispersion wave methods for solving the wave equation reduce the computational overhead and memory requirements [17], [26]. One of these methods is the adaptive rectangular decomposition (ARD) technique [22, 19], which performs three-dimensional acoustic wave propagation for homogeneous media (implying a spatially-invariant speed of sound). ARD is a domain decomposition technique that partitions a scene in rectangular (cuboidal in 3D) regions, computes local pressure fields in each partition, and combines them to compute the global pressure field using appropriate interface operators. Previously, ARD has been used to perform acoustic simulations on small indoor and outdoor scenes for a maximum frequency of 1 kHz using only a few gigabytes of memory on a high-end desktop machine. However, performing accurate acoustic simulation for large acoustic spaces up to the full auditory range of human hearing still requires terabytes of memory (e.g., which may be provided by one or more special purpose computer machines). Therefore, there is a need to develop efficient parallel algorithms, scalable on distributed memory clusters, to perform these large-scale acoustic simulations.
Accordingly, there exists a need for systems, methods, and computer readable media for utilizing parallel adaptive rectangular decomposition to perform acoustic simulations.